System and method for forecasting fuel consumption for indoor thermal conditioning using thermal performance forecast approach with the aid of a digital computer

ABSTRACT

A system and method for forecasting fuel consumption for indoor thermal conditioning using thermal performance forecast approach with the aid of a digital computer are provided. Average daily outdoor temperatures for a time period are obtained. Historical daily fuel consumption for the time period is obtained. The historical daily fuel consumption is converted into an average daily fuel usage rates for the time period. A continuous frequency distribution of occurrences of the average daily outdoor temperatures is generated. A plot of the daily fuel usage rates versus the average daily outdoor temperatures is created. Fuel consumption for at least a portion of the time period is calculated based on sampling the daily fuel usage rate along a range of average daily outdoor temperatures times the temperatures&#39; respective frequencies of occurrence.

CROSS-REFERENCE TO RELATED APPLICATION

This patent application is a continuation of U.S. Pat. No. 10,359,206,issued Jul. 23, 2019, the priority date of which is claimed and thedisclosure of which is incorporated by reference.

FIELD

This application relates in general to energy conservation and, inparticular, to a system and method for forecasting fuel consumption forindoor thermal conditioning using thermal performance forecast approachwith the aid of a digital computer.

BACKGROUND

Thermal conditioning provides heating, air exchange, and cooled(dehumidified) air within a building to maintain an interior temperatureand air quality appropriate to the comfort and other needs or goals ofthe occupants. Thermal conditioning may be provided through acentralized forced air, ducted heating, ventilating, and airconditioning (HVAC) system, through discrete components, such aselectric baseboard heaters for heat, ceiling or area fans for aircirculation, and window air conditioners for cooling, heat pumps forheating and cooling, or through a combination of thermal conditioningdevices. However, for clarity herein, all forms of thermal conditioningequipment, whether a single do-all installed system or individualcontributors, will be termed HVAC systems, unless specifically notedotherwise.

The types of thermal conditioning that are required inside of abuilding, whether heating, ventilating, or cooling, are largely dictatedby the climate of the region in which the building is located and theseason of the year. In some regions, like Hawaii, air conditioning mightbe used year round, if at all, while in other regions, such as thePacific Northwest, moderate summer temperatures may obviate the need forair conditioning and heating may be necessary only during the wintermonths. Nevertheless, with every type of thermal conditioning, the costsof seasonal energy or fuel consumption are directly tied to thebuilding's thermal efficiency. For instance, a poorly insulated buildingwith significant sealing problems will require more overall HVAC usageto maintain a desired inside temperature than would a comparably-sizedbut well-insulated and sealed structure. As well, HVAC systemefficiency, heating and cooling season duration, differences betweenindoor and outdoor temperatures, and internal temperature gainsattributable to heat created by internal sources can further influenceseasonal fuel consumption in addition to a building's thermalefficiency.

Forecasting seasonal fuel consumption for indoor thermal conditioning,as well as changes to the fuel usage rate triggered by proposedinvestments in the building or thermal conditioning equipment, must takeinto account the foregoing parameters. While the latter parameters aretypically obtainable by the average consumer, quantifying a building'sthermal conductivity remains a non-trivial task. Often, gauging thermalconductivity requires a formal energy audit of building exteriorsurfaces and their materials' thermal insulating properties, orundertaking empirical testing of the building envelope's heat loss andgain.

Once the building's thermal conductivity (UA^(Total)) and theaccompanying parameters are known, seasonal fuel consumption can beestimated. For instance, a time series modelling approach can be used toforecast fuel consumption for heating and cooling, such as described incommonly-assigned U.S. Pat. No. 10,339,232, issued Jul. 2, 2019, thedisclosure of which is incorporated by reference. In one such approach,the concept of balance point thermal conductivity replaces balance pointtemperature and solar savings fraction, and the resulting estimate offuel consumption reflects a separation of thermal conductivity intointernal heating gains and auxiliary heating. In a second approach,three building-specific parameters are first empirically derived throughshort-duration testing, after which those three parameters are used tosimulate a time series of indoor building temperatures and fuelconsumption. While both approaches usefully predict seasonal fuelconsumption, as time series-focused models, neither lends itself well tocomparative and intuitive visualizations of seasonal fuel consumptionand of the effects of proposed changes to thermal conditioningcomponents or properties.

Alternatively, heating season fuel consumption can be determined usingthe Heating Degree Day (HDD) approach, which derives fuel consumptionfor heating needs from measurements of outside air temperature for agiven structure at a specific location. An analogous Cooling Degree Day(CDD) approach exists for deriving seasonal fuel consumption forcooling. Although widely used, the HDD approach has three notablelimitations. First, the HDD approach incorrectly assumes that heatingseason fuel consumption is linear with outside temperature. Second, theHDD approach often neglects the effect of thermal insulation on abuilding's balance point temperature, which is the indoor temperature atwhich heat gained from internal sources equals heat lost through thebuilding's envelope. In practice, heavily insulated buildings have alower balance point temperature than is typically assumed by the HDDapproach. Third, required heating (or cooling) depends upon factorsother than outdoor temperature alone, one factor of which is the amountof solar radiation reaching the interior of a building. In addition tothese three procedural weaknesses, the HDD approach fails to separateinput assumptions from weather data, nor is intuitive to the averageconsumer. (For clarity, the Heating Degree Day and Cooling Degree Dayapproaches will simply be called the Degree Day approach, unlessindicated to the contrary.)

Therefore, a need remains for a practical and comprehendible model forpredicting a building's seasonal fuel consumption that is readilyvisualizable.

A further need remains for a practical and comprehendible model forpredicting changes to a building's seasonal fuel consumption in light ofpossible changes to the building's thermal envelope or thermalconditioning componentry.

SUMMARY

A Thermal Performance Forecast approach is described that can be used toforecast heating and cooling fuel consumption based on changes to userpreferences and building-specific parameters that include desired indoortemperature (specified by adjusting the temperature setting of athermostat), building insulation, HVAC system efficiency, and internalheating gains. A simplified version of the Thermal Performance Forecastapproach, called the Approximated Thermal Performance Forecast, providesa single equation that accepts two fundamental input parameters and fourratios that express the relationship between the existing andpost-change variables for the building properties to estimate futurefuel consumption. The Approximated Thermal Performance Forecast approachmarginally sacrifices accuracy for a simplified forecast. In addition,the thermal conductivity, effective window area, and thermal mass of abuilding can be determined using different combinations of utilityconsumption, outdoor temperature data, indoor temperature data, internalheating gains data, and HVAC system efficiency as inputs.

In one embodiment, a system and method for forecasting fuel consumptionfor indoor thermal conditioning using thermal performance forecastapproach with the aid of a digital computer are provided. Average dailyoutdoor temperatures for a time period are obtained. Historical dailyfuel consumption for the time period is obtained. The historical dailyfuel consumption is converted into an average daily fuel usage rates forthe time period. A continuous frequency distribution of occurrences ofthe average daily outdoor temperatures is generated. A plot of the dailyfuel usage rates versus the average daily outdoor temperatures iscreated. Fuel consumption for at least a portion of the time period iscalculated based on sampling the daily fuel usage rate along a range ofaverage daily outdoor temperatures times the temperatures' respectivefrequencies of occurrence.

Both the Thermal Performance Forecast approach and Approximated ThermalPerformance Forecast approach provide superior alternatives to theDegree Day approach in estimating seasonal fuel consumption. The ThermalPerformance Forecast approach addresses the shortcomings of the DegreeDay approach, while retaining the latter's simplicity. In addition, theThermal Performance Forecast approach provides a comprehensive thermalanalysis in an easily understood format that can provide valuableinsights to residential and commercial end users, utilities, and policymakers.

Moreover, both approaches are significant improvements upon conventionalmethodologies and offer valuable analytical tools. Both of theseapproaches offer side-by-side comparison of alternatives scenarios, afeature not provided by conventional techniques. The ability to makeside-by-side comparisons enables customers to ensure that theirinvestments result in the biggest impact per dollar spent.

Finally, fundamental building thermal property parameters, includingthermal conductivity, effective window area, and thermal mass can bedetermined without the need for on-site visits or empirical testing,which significantly streamlines energy analysis. For instance, theseparameters can be input into time series modelling approaches toforecast hourly fuel consumption.

Still other embodiments will become readily apparent to those skilled inthe art from the following detailed description, wherein are describedembodiments by way of illustrating the best mode contemplated. As willbe realized, other and different embodiments are possible and theembodiments' several details are capable of modifications in variousobvious respects, all without departing from their spirit and the scope.Accordingly, the drawings and detailed description are to be regarded asillustrative in nature and not as restrictive.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a functional block diagram showing heating losses and gainsrelative to a structure.

FIG. 2 is a flow diagram showing a prior art method for modelingperiodic building energy consumption for thermal conditioning using theDegree Day approach.

FIG. 3 is a flow diagram showing a method for forecasting seasonal fuelconsumption for indoor thermal conditioning using the ThermalPerformance Forecast approach with the aid of a digital computer inaccordance with one embodiment.

FIG. 4 is a graph showing, by way of example, seasonal thermalconditioning needs as determined through the Degree Day approach.

FIG. 5 is a graph showing, by way of example, seasonal thermalconditioning needs and annual fuel consumption as determined through theThermal Performance Forecast approach.

FIG. 6 is a graph showing, by way of example, the base thermalconditioning needs and annual fuel consumption for a building.

FIG. 7 is a graph showing, by way of example, the thermal conditioningneeds and annual fuel consumption for the building of FIG. 6 followingaddition of a smart thermostat.

FIG. 8 is a graph showing, by way of example, the thermal conditioningneeds and annual fuel consumption for the building of FIG. 7 followingaddition of a triple heater efficiency.

FIG. 9 is a graph showing, by way of example, the thermal conditioningneeds and annual fuel consumption for the building of FIG. 8 followingaddition of double air conditioning efficiency.

FIG. 10 is a graph showing, by way of example, the thermal conditioningneeds and annual fuel consumption for the building of FIG. 9 followingaddition of double shell efficiency.

FIG. 11 is a graph showing, by way of example, the thermal conditioningneeds and annual fuel consumption for the building of FIG. 10 followingremoval of half of the internal gains.

FIG. 12 is a flow diagram showing a method for forecasting seasonal fuelconsumption for indoor thermal conditioning using the ApproximatedThermal Performance Forecast approach with the aid of a digital computerin accordance with a further embodiment.

FIG. 13 is a set of graphs showing, by way of examples, normalizedresults for seasonal fuel consumption forecasts generated by theApproximated Thermal Performance Forecast and Degree Day approaches forfive different cities.

FIG. 14 is a flow diagram showing a routine for determining adjustedinternal gains for use with the method of FIG. 12.

FIG. 15 is a graph showing, by way of example, daily heating fuelconsumption versus average outdoor temperature for the heating seasonfor the efficient house.

FIG. 16 is a graph showing, by way of example, predicted versus measureddaily fuel consumption for the efficient house with thermal massexcluded.

FIG. 17 is a graph showing, by way of example, predicted versus measureddaily fuel consumption for the efficient house with thermal massincluded.

FIG. 18 is a graph showing, by way of example, predicted versus measureddaily fuel consumption for the efficient house over time.

FIG. 19 is a graph showing, by way of example, daily heating fuelconsumption versus average outdoor temperature for the heating seasonfor the inefficient house.

FIG. 20 is a graph showing, by way of example, predicted versus measureddaily fuel consumption for the inefficient house with thermal massexcluded.

FIG. 21 is a graph showing, by way of example, predicted versus measureddaily fuel consumption for the inefficient house with thermal massincluded.

FIG. 22 is a graph showing, by way of example, predicted versus measureddaily fuel consumption for the inefficient house over time.

FIG. 23 is a system for forecasting seasonal fuel consumption for indoorthermal conditioning with the aid of a digital computer in accordancewith one embodiment.

DETAILED DESCRIPTION

Seasonal and annual fuel consumption for the thermal conditioning of abuilding can be forecast using a Thermal Performance Forecast approach,which uses empirically-derived inputs and is intuitive enough for theaverage consumer to apply and understand. The approach offers a unifiedsolution for both heating and cooling seasons with building-specificforecasts that provide clarity about how proposed energy investments mayaffect building performance and side-by-side comparisons for a widevariety of building upgrades, including proposed changes to thermalconditioning components or properties.

In a further embodiment, a simplified version, the Approximated ThermalPerformance Forecast approach, is easier to perform while minimallyreducing forecasting accuracy. Only two input parameters, the amount ofseasonal fuel consumed for heating (or cooling) and adjusted internalgains, are required. One or more changes to thermal conductivity,desired indoor temperature, internal heating gains, and HVAC systemefficiency can then be modeled to evaluate their effects on seasonalfuel consumption. This forecast is useful to consumers wishing tooptimize building improvements, businesses hoping to improve occupantcomfort while reducing costs, and policymakers seeking to betterunderstand which building improvements are worthy of incentives.

By way of introduction, the foundational building blocks underpinningthe Thermal Performance Forecast approach will now be discussed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a functional block diagram 10 showing heating losses and gainsrelative to a structure 11. Inefficiencies in the shell 12 (or envelope)of a structure 11 can result in losses in interior heating 14, whereasinternal gains Q^(Internal) 13 in heating generally originate eitherfrom sources within (or internal to) the structure 11, including wasteheat from operating electric appliances Q^(Electric) 15 in the structure11, the heat from occupants Q^(Occupants) 16 of the structure 11, andthe amount of solar radiation or solar gains Q^(Solar) 17 reaching theinterior of the structure 11, or from auxiliary heating sources 18 thatare specifically intended to provide heat to the structure's interior.

Internal Gains

Internal gains Q^(Internal) 13 represent the heat that a building gainsinternally that are attributable to sources within the building. The HDDapproach only considers waste heat from operating electric appliancesQ^(Electric) and heat generated by a building's occupants Q^(Occupants).By contrast, internal gains Q^(Internal) for the Thermal PerformanceForecast approach includes internal gains from electricity Q^(Electric)15 and internal gains from occupants Q^(Occupants) 16, and also factorsin internal solar gains Q^(Solar) 17, such that:Q ^(Internal) =Q ^(Electric) +Q ^(Occupants) +Q ^(Solar)  (1)Solar Gains and Effective Window Area

Solar energy that enters through windows, doors, and other openings andsurfaces in a building (opaque or non-opaque) will heat the interior.Solar gains Q^(Solar) equal the amount of solar radiation reaching theinterior of a building. The source of the solar data must be consistentas between calculating the effective window area and forecastingseasonal fuel consumption. For instance, if global horizontal irradiance(GHI) is used as the solar data for the effective window areacalculation, the GHI should also be used in the forecasting model. Solargains Q^(solar) can be estimated based upon the effective window area W(in m²) multiplied by the available solar resource Solar (in kWh/m²):Q ^(Solar)=(W)(Solar)  (2)In turn, effective window area W can be calculated by substitutingEquation (2) into Equation (1) and solving for W:

$\begin{matrix}{W = \frac{Q^{Internal} - \left( {Q^{Electric} + Q^{Occupants}} \right)}{Solar}} & (3)\end{matrix}$Effective window area W can also be empirically derived through a seriesof sequentially-performed short duration tests, such as described incommonly-assigned U.S. Pat. No. 10,339,232, cited supra, which also setsforth the basis of Equation (2) for estimating the solar gains Q^(Solar)using the effective window area W.

Equation (3) implies that effective window area W can be calculatedbased on overall internal gains Q^(Internal), internal gains fromelectricity Q^(Electric), internal gains from occupants Q^(Occupants)and the available solar resource Solar.

Balance Point Temperature

The balance point temperature T^(Balance-Point) is the indoortemperature at which heat gained from internal sources, including thesolar gains Q^(Solar) (but not in the Degree Day approach) equals heatlost through the building's envelope. The balance point temperature 19can be derived from internal gains 13. When applied over a heating (orcooling) season, internal gains 13 equals the building's thermalconductivity UA^(Total) multiplied by the difference between the averageindoor temperature T ^(Indoor) and the balance point temperature 19applicable to the heating (or cooling) season, multiplied by the numberof hours H in the heating (or cooling) season:Q ^(Internal) =UA ^(Total)( T ^(Indoor) −T ^(Balance-Point))H  (4)

Internal gains Q^(Internal) can be converted to average internal gains Q^(Internal) by dividing by the number of hours in the heating (orcooling) season. Solving for balance point temperatureT^(Balance-Point):

$\begin{matrix}{T^{\text{Balance}\text{-}\text{Point}} = {{\overset{\_}{T}}^{Indoor} - \frac{{\overset{\_}{Q}}^{Internal}}{{UA}^{Total}}}} & (5)\end{matrix}$

A building's overall thermal conductivity (UA^(Total)) can be estimatedthrough an energy audit that first measures or verifies the surfaceareas of all non-homogeneous exterior-facing surfaces and thendetermines the insulating properties of the materials used within. Thosefindings are combined with the difference between the indoor and outdoortemperature to arrive at the building's overall thermal conductivity.Alternatively, UA^(Total) can be empirically determined through ashort-duration controlled test, such as described in commonly-assignedU.S. Pat. No. 10,024,733, issued Jul. 17, 2018, the disclosure of whichis incorporated by reference. The controlled test is performed with aswitched heating source over a test period and overall thermalperformance is estimated by balancing the heat gained within thebuilding with the heat lost during the test period. Still other ways todetermine UA^(Total) are possible.

Adjusted Internal Gains

Internal gains Q^(Internal) can be converted into adjusted internalgains Q^(Adj.Internal) by adjusting for season and HVAC systemefficiency. The season adjustment causes internal gains 13 to either besubtracted from fuel requirements during the heating season or added tofuel requirements during the cooling season. The season adjustment ismade by multiplying internal gains Q^(Internal) by a binary flagHeatOrCool that is set to 1 for the heating season and to −1 for thecooling season. The HVAC system efficiency adjustment reflects theequivalent amount of fuel required to deliver the same amount of heating(or cooling) based on the HVAC system efficiency η^(HVAC). To convertinternal gains Q^(Internal) into adjusted internal gainsQ^(Adj.Internal):

$\begin{matrix}{Q^{{Adj}.\;{Internal}} = {({HeatOrCool})\left( \frac{Q^{Internal}}{\eta^{HVAC}} \right)}} & (6)\end{matrix}$Substituting in Equation (4):

$\begin{matrix}{Q^{{Adj}.\;{Internal}} = {({HeatOrCool})\left( \frac{{UA}^{Total}}{\eta^{HVAC}} \right)\left( {{\overset{\_}{T}}^{Indoor} - T^{\text{Balance}\text{-}\text{Point}}} \right)H}} & (7)\end{matrix}$

Thermal Mass

A building's thermal mass M represents another source of heating (orcooling) when the building's indoor temperature is not in equilibriumdue to heat being stored in (or drawn from) the building. The effects ofthermal mass 20 are more impactful over shorter time periods, such as aday or less. A building's heat capacity (in kWh) that is associated witha change in indoor temperature equals the building's thermal mass M (inkWh/° F.) multiplied by the difference between the ending indoortemperature T_(End Time) ^(Indoor) and starting indoor temperatureT_(Start Time) ^(Indoor):Q ^(Thermal Mass) =M(T _(Start Time) ^(Indoor) −T _(End Time)^(Indoor))  (8)This result is described more fully in commonly-assigned U.S. Pat. No.10,339,232, cited supra.Comparison of Approaches

The Degree Day approach derives fuel consumption for heating and coolingneeds from measurements of outside air temperature for a given structureat a specific location, while the Thermal Performance Forecast approachuses empirically-derived inputs to generate building-specific forecastsof seasonal fuel consumption in a weather data-independent fashion.

Degree Day Approach

First, consider the Degree Day approach. FIG. 2 is a flow diagramshowing a prior art method 30 for modeling periodic building energyconsumption for thermal conditioning using the Degree Day approach.Execution of the software can be performed with the assistance of acomputer system.

First, average daily outdoor temperatures are obtained over a period ofinterest, such as a year, as input data (step 31). Balance pointtemperatures 19 for the structure are then identified (step 32). Duringthe heating season, the balance point temperature 19 is the temperatureat which the internal gains 13 provide a sufficient amount of heat suchthat auxiliary heating 18 is only required to meet the heating needsbelow this temperature. During the cooling season, the balance pointtemperature 19 is the temperature at which the air conditioning systemmust be operated to remove the internal gains 13. The number of degreedays is computed over the entire period (step 33). The heating degreedays equal the sum of average daily temperatures below the balance pointtemperature 19, that is, 63° F. in FIG. 4, and the cooling degree daysequal the sum of average daily temperatures above the balance pointtemperature 19, that is, 67° F. in FIG. 4. Annual fuel consumption isthen calculated (step 34) by combining number of heating and coolingdegree days with the building's thermal conductivity UA^(Total) and HVACsystem efficiency η^(HVAC). Optionally, for purposes of visualizationand understanding, as further discussed infra with reference to FIG. 4,the heating and cooling fuel consumption can be plotted against theaverage daily outdoor temperatures (step 35). Finally, the annual fuelconsumption is adjusted for internal solar gains 17 (step 36).

Thermal Performance Forecast Approach

Next, consider the Thermal Performance Forecast approach. FIG. 3 is aflow diagram showing a method 40 for forecasting seasonal fuelconsumption for indoor thermal conditioning using the ThermalPerformance Forecast approach with the aid of a digital computer inaccordance with one embodiment. Execution of the software can beperformed with the assistance of a computer system, such as furtherdescribed infra with reference to FIG. 23, as a series of process ormethod modules or steps.

First, balance point temperatures 19 for the structure are identified(step 41). The balance point temperatures 19 can be identified in thesame fashion as for the Degree Day approach, but with the inclusion ofinternal solar gains 17, as discussed supra with reference to Equation(1). Ordinarily, there will be a different balance point temperature 19for the heating season versus the cooling season. If fuel consumption isbeing forecast over an entire year, both balance point temperatures 19will be needed. Otherwise, only the balance point temperature 19applicable to the season for which fuel consumption is being forecastwill be required.

Next, the average daily outdoor temperatures are obtained over anearlier period of interest, such as a year or just for the applicable(heating or cooling) season, as input data (step 42). If the outsidetemperature data is in an hourly format, the outside temperature must beconverted into average daily values. Historical daily fuel consumptionis obtained for the applicable season (step 43), which reflects the fuelconsumed to maintain the building's indoor temperature between thebalance point temperature 19 and the average daily outdoor temperatures.The historical daily fuel consumption can be measured, for example,directly from a customer's utility bills. The historical daily fuelconsumption is then converted into an average daily fuel usage rate(step 44) by dividing by 24, that is, energy in kWh/day divided by 24hours/day results in units of kW. A continuous frequency distribution ofthe occurrences of average daily outdoor temperatures is generated (step45). The average daily fuel usage rate is also plotted versus theaverage daily outdoor temperature (step 46), as further discussed infrawith reference to FIG. 5. Finally, seasonal fuel consumption iscalculated (step 47) as the fuel usage rate sampled along the range ofaverage daily outdoor temperatures times the temperatures' respectivefrequencies of occurrence, as per Equation (14), discussed in detailinfra.

Differences

While both methodologies can generate forecasts of seasonal fuelconsumption, the Degree Day approach overly relies on outdoortemperature, which is assumed to be as linear to fuel consumption and isconsidered exclusive to other factors, including the effects of thermalinsulation on a building's balance point temperature 19 and internalsolar gains 17. This overreliance on outdoor temperature is reflected inthe manner in which Degree Day forecasting results are visualized. Tocompare the Degree Day and Thermal Performance Forecast approaches, oneyear of historical outdoor temperature data was obtained fromSolarAnywhere®, a Web-based service operated by Clean Power Research,L.L.C., Napa, Calif., for Washington, D.C. for the time period runningfrom Jan. 1, 2015 to Dec. 31, 2015. Seasonal thermal conditioning needsand, where applicable, fuel consumption were determined by each approachand visualized.

For the Degree Day approach, the hourly outside temperature data wasfirst converted into average daily values. FIG. 4 is a graph 50 showing,by way of example, seasonal thermal conditioning needs as determinedthrough the Degree Day approach. The x-axis 51 represents the month.They-axis 52 represents the temperature (in ° F.). The average dailytemperatures 53 were plotted over the course of the year to reflect theaverage temperature that was recorded for each day. During the heatingseason, the balance point temperature 54 was 63° F. based on an indoortemperature of 68° F., which meant that the heater had to be operatedwhen the average daily temperature was below 63° F. The total number ofheating degree days (HDD) 55 equal the sum of the average dailytemperatures below 63° F. across the year. Similarly, during the coolingseason, the balance point temperature 54 was 67° F. based on an indoortemperature of 72°, which meant that the air conditioning had to beoperated when the temperature is above 67° F. The total number ofcooling degree days (CDD) 56 equal the sum of the average dailytemperatures above 67° F. across the year.

When presented in this fashion, the Degree Day approach allows seasonalthermal conditioning needs to be visualized in terms of heating andcooling degree days. Here, the key weather-related inputs are the numberof heating and cooling degree days; however, the approach interminglesweather data with user preferences, specifically, the desired indoortemperature, and building-specific parameters, including internalheating gains and building shell losses. Consequently, changes to any ofthese non-weather data values can affect the number of heating andcooling degree days, thus triggering a recalculation with the resultthat detailed average daily outdoor temperature data must be retained toaccurately re-calculate the seasonal fuel consumption.

For the Thermal Performance Forecast approach, the hourly outsidetemperature data was converted into average daily values and acontinuous frequency distribution was generated. FIG. 5 is a graph 60showing, by way of example, seasonal thermal conditioning needs andannual fuel consumption as determined through the Thermal PerformanceForecast approach. The x-axis 61 represents the temperature 61 (in °F.). There are two y-axes 62, 63. The right-hand y-axis 62 representsthe value of the average daily temperature's frequency distribution 64(as a percentile), which corresponds to a plot of the frequency ofoccurrence distribution of the average daily temperatures 64 over therange of average daily temperatures. The left-hand y-axis 63 representsthe average daily fuel usage rate (in kW), which corresponds to plots offuel consumption respectively for heating 65 and cooling 66 over therange of the average daily temperatures. Instantaneous fuel consumptioncan be calculated by multiplying the fuel usage rate for a given averagedaily temperature by the frequency of occurrence for that temperature.For instance, an average daily temperature of 25° F. would require fuelusage rate of slightly less than 10 kW for roughly 4% of the one-yeartime period.

The Thermal Performance Forecast graph 60 is more intuitive tounderstand than the Degree Day graph 50. Here, the key weather-relatedinput to the Thermal Performance Forecast is the continuous frequencydistribution of the average daily temperatures. Importantly, the plotsof fuel usage rate for heating 65 and cooling 66 are superimposed overthe frequency distribution 64, which keeps the weather data separatefrom factors that can affect fuel usage rate, such as the structure'sthermal conductivity, desired indoor temperature, internal heatinggains, and HVAC system efficiency. Moreover, the separation of weatherdata from such factors enables proposed changes to be evaluated by asimple visual inspection of the graph 60. For instance, heating orcooling costs are high if the respective slopes of the fuel usage ratesfor heating 65 or cooling 66 are steep. Conversely, heating or coolingcosts are low if the slopes are gentle. This aspect of the ThermalPerformance Forecast graph 60 allows consumers to make simpleside-by-side comparisons of proposed investments in the building orthermal conditioning equipment. If a consumer were trying to evaluatethe cost savings by installing a Smart Thermostat, for example, theDegree Day approach requires a recalculation due to the intermingling ofweather data with user preferences and building-specific parameters,whereas the Thermal Performance Forecast approach does not require arecalculation and cost savings can be readily visualized by the changesto the slopes of the plots of fuel usage rates.

Annual Fuel Consumption (Heating Season)

Consider the amount of fuel consumed during the heating season. Assumethat the internal gains 13 are constant throughout the heating seasonand that HVAC system efficiency η^(HVAC) is only dependent upon thedifference between indoor and outdoor temperature and not on absoluteoutdoor temperature. Note that this assumption would be accurate for afuel-burning technology; however, a modification to that assumption maybe required for heat pump technologies since their efficiency isdependent upon outdoor temperature.

With the Thermal Performance Forecast approach, annual heating fuelconsumption, per Equation (9), equals the sum of the product of theheating fuel usage rate 65 multiplied by frequency of occurrence 64multiplied by number of hours in the year. Heating fuel usage rate 65equals the amount of heat that needs to be produced to replace heat lostthrough the structure's envelope divided by HVAC system efficiencyη^(HVAC) Annual heating fuel consumption Q^(Fuel) can be solved byintegration when the temperature increment is small; the integrationstarts at a temperature of 0 degrees Rankine (° R), that is, absolutezero plus approximately −460° F., and ends when the outdoor temperatureequals the heating season balance point temperature 67:

$\begin{matrix}{Q^{Fuel} = {\int_{0{^\circ}\mspace{11mu} R}^{T^{\text{Balance}\text{-}\text{Point}}}\frac{{{UA}^{Total}\left( {T^{\text{Balance}\text{-}\text{Point}} - T^{Outdoor}} \right)}{f(T)}(8760){dT}}{\eta^{{HVAC} - {Heating}}}}} & (9)\end{matrix}$where η^(HVAC-Heating) is the efficiency of the HVAC system for heating.

The temperature frequency distribution function can be normalized bydividing by the cumulative frequency distribution evaluated from 0° R tothe heating balance point temperature 67, that is,F(T^(Heating Balance-Point)):

$\begin{matrix}{{\hat{f}(T)} = \frac{f(T)}{F\left( T^{\text{Balance}\text{-}\text{Point}} \right)}} & (10)\end{matrix}$Solve Equation (10) for f(T), substitute in Equation (9), and factor outconstants:

$\begin{matrix}{Q^{Fuel} = {\left\lbrack \frac{{UA}^{Total}{F\left( T^{{Balance} - {Point}} \right)}(8760)}{\eta^{{HVAC} - {Heating}}} \right\rbrack{\quad\left\lbrack {\int_{0{^\circ}\mspace{11mu} R}^{T^{{Balance} - {Point}}}{\left( {T^{{Balance} - {Point}} - T^{Outdoor}} \right){\hat{f}(T)}{dT}}} \right\rbrack}}} & (11)\end{matrix}$

The solution to the integration equals the balance point temperature 67minus the outdoor temperature averaged up to the point where outdoortemperature equals the balance point temperature 67:

$\begin{matrix}{Q^{Fuel} = \frac{{{UA}^{Total}\left( {T^{{Balance} - {Point}} - {\overset{\_}{T}}^{Outdoor}} \right)}(H)}{\eta^{{HVAC} - {Heating}}}} & (12)\end{matrix}$where H is the number of hours in the heating season.

Substitute Equation (5) into Equation (12) and simplify:

$\begin{matrix}{Q^{Fuel} = \frac{{{{UA}^{Total}\left( {{\overset{\_}{T}}^{Indoor} - {\overset{\_}{T}}^{Outdoor}} \right)}(H)} - Q^{Internal}}{\eta^{{HVAC} - {Heating}}}} & (13)\end{matrix}$where Q^(Internal) equals the overall internal gains 13 over the heatingseason.Annual Fuel Consumption (Heating and Cooling Seasons)

A similar approach to forecasting the amount of fuel consumed during thecooling season and the results from the two seasons can be unified toprovide a forecast of annual fuel consumption. Equation (13) isgeneralized by multiplying by the binary flag HeatOrCool. Internal gains13 can then be factored out of the equation and converted to adjustedinternal gains:

$\begin{matrix}\begin{matrix}{Q^{Fuel} = {\frac{({HeatOrCool})\left( {UA}^{Total} \right)\left( {{\overset{\_}{T}}^{Indoor} - {\overset{\_}{T}}^{Outdoor}} \right)(H)}{\eta^{HVAC}} - Q^{{Adj}.{Internal}}}}\end{matrix} & (14)\end{matrix}$Equation (14) can be rearranged as:

$\begin{matrix}{{Q^{Fuel} + Q^{{Adj}.{Internal}}} = \frac{({HeatOrCool})\left( {UA}^{Total} \right)\left( {{\overset{\_}{T}}^{Indoor} - {\overset{\_}{T}}^{Outdoor}} \right)(H)}{\eta^{HVAC}}} & (15)\end{matrix}$

Equation (15) corrects the assumption followed by the Degree Dayapproach that heating fuel consumption is linear with temperature forboth heating and cooling situations, which clarifies that the sum offuel consumption Q^(Fuel) plus fuel representing adjusted internal gainsQ^(Adj.Internal) is linear with temperature.

The effects of changes to user preferences and building-specificparameters on heating and cooling fuel consumption are visuallydepictable with the approach taken by the Thermal Performance Forecast.FIG. 6 through FIG. 11 graph the cumulative effect of five separateinvestments on a building. As discussed supra with reference to FIG. 5,in each of these graphs, the x-axis 61 represents the temperature (in °F.), the right-hand y-axis represents the value of the average dailytemperature's frequency distribution (as a percentile), and theleft-hand y-axis represents fuel usage rate (in kW). In all of thegraphs, there are two key characteristics that differentiate the ThermalPerformance Forecast and the Degree Day approaches. First, as the resultof each investment, the balance point temperatures may change.Similarly, the superimposed slopes of the plots of heating and coolingfuel usage rates may also change, while the distribution of the weatherdata remains the same.

The graphs demonstrate the cumulative effects of changes to differentfactors that affect the thermal conditioning of the building, includingthe structure's thermal conductivity UA^(Total) desired indoortemperature T ^(Indoor) (treated as a value averaged over the applicableseason), internal heating gains Q^(Internal) (which results in arecalculation of adjusted internal gains Q^(Adj.Internal)), and HVACsystem efficiency η^(HVAC), and the forecast seasonal fuel consumptionchanges in light of each change. Referring first to the graph 70 in FIG.6, the base thermal conditioning needs and annual (seasonal) fuelconsumption for the building are shown. The balance point temperatures71 are respectively 63° F. and 67° F. for heating and cooling withheating fuel usage rate 72 close to 10 kW at 25° F. and cooling fuelusage rate 73 of about 2.5 kW at 100° F. Referring next to the graph 80in FIG. 7, a smart thermostat has been added with the result that thebalance point temperature 81 for heating has been lowered to 61° F.while the balance point temperature 81 for cooling has been raised to69° F. These changes result in new desired indoor temperatures that aretreated as averaged values for purposes of forecasting seasonal fuelconsumption. Referring next to the graph 90 in FIG. 8, triple heaterefficiency has been added by converting from a fuel-based heater to heatpump-based heating. The balance point temperatures 91 and cooling fuelusage rate 93 remain unchanged, while the slope of the plot of heatingfuel usage rate 92 has a dramatically flatter slope with the fuel usagerate being about 2.5 kW at 25° F. Referring next to the graph 100 inFIG. 9, double air conditioning efficiency has been added by integratingthe air conditioning system with the heat pump. Here, the balance pointtemperatures 101 and heating fuel usage rate 102 remain unchanged, whilethe slope of the plot of cooling fuel usage rate 103 has a slope half assteep as before with a fuel usage rate of about 1.25 kW at 100° F.Referring next to the graph 110 in FIG. 10, the R-values of thebuilding's walls and steps to reduce infiltration have been taken toprovide double shell efficiency. Now, the balance point temperatures 111for heating and cooling respectively are 56° F. and 64°. Finally,referring to the graph 120 of FIG. 11, half of the internal gains 13within the building have been removed by reducing the heat generated byelectrical appliances by improving the types of electrical devices,turning off unused or unneeded equipment, switching to LED lighting, andmaking other similar changes. The balance point temperatures 121 forheating and cooling respectively are 61° F. and 69° F. The higherbalance point temperatures 121 was triggered by the need to make up forthe decrease in existing heat within the building due to the reductionin internal gains 13.

To summarize, in contrast to the Degree Day approach, the ThermalPerformance Forecast methodology separates weather data fromuser-preferences and building-specific parameters. This separationprovides several benefits that include:

-   -   Clear visual representation: the effects of building-related        investments on heating and cooling fuel consumption are readily        visualized.    -   Simplified estimation of fuel consumption: Fuel consumption can        be estimated under a wide range of scenarios using a simple        equation.    -   Observable parameters: Heating and cooling fuel consumption        versus average daily temperature is directly observable.        Approximated Thermal Performance Forecast Approach

The Thermal Performance Forecast approach can be used to forecastheating and cooling fuel consumption based on changes to userpreferences and building-specific parameters that include desired indoortemperature (specified by selecting a new temperature setting for thethermostat), building insulation, HVAC system efficiency, and internalheating gains. This section derives a simplified version of the analysisthat is referred to as the Approximated Thermal Performance Forecastapproach. Equation (14) forecasts fuel consumption based on a number ofinput variables for a building's properties that can also be used topredict future fuel consumption after energy consumption investment havebeen made.

Let ‘*’ denote each existing input variable following a proposed changeand assume that the changes do not affect the duration of the heating orcooling seasons, such that the average outdoor temperature remainsunaffected. Future fuel consumption Q^(Fuel)* can be predicted asfollows:

$\begin{matrix}{Q^{{Fuel}^{*}} = {\frac{({HeatOrCool})\left( {UA}^{{Total}^{*}} \right)\left( {{\overset{\_}{T}}^{*\;{Indoor}} - {\overset{\_}{T}}^{Outdoor}} \right)(H)}{\eta^{{HVAC}^{*}}} - Q^{{Adj}.{Internal}^{*}}}} & (16)\end{matrix}$where UA^(Total)* represents post-change thermal conductivity, T*^(Indoor) represents post-change average indoor temperature, η^(HVAC)*represents post-change HVAC system efficiency, and Q^(Adj.Internal)*represents post-change adjusted internal gains.

Next, define four ratio terms that express the relationships between theexisting and post-change variables for the building properties andassume that none of the existing values would make the denominatorsequal zero, so that all of the ratios are well defined:

$\begin{matrix}{{R^{UA} = \frac{{UA}^{{Total}^{*}}}{{UA}^{Total}}}{R^{Temp} = \frac{\left( {{\overset{\_}{T}}^{*{Indoor}} - {\overset{\_}{T}}^{Outdoor}} \right)}{\left( {{\overset{\_}{T}}^{Indoor} - {\overset{\_}{T}}^{Outdoor}} \right)}}{R^{\eta} = \frac{\eta^{{HVAC}^{*}}}{\eta^{HVAC}}}{R^{Internal} = \frac{Q^{{Internal}^{*}}}{Q^{Internal}}}} & (17)\end{matrix}$Rearrange the terms in Equation (17):

$\begin{matrix}{{UA}^{{Total}^{*}} = {{UA}^{Total}R^{UA}}} & (18) \\{\left( {{\overset{\_}{T}}^{*\;{Indoor}} - {\overset{\_}{T}}^{Outdoor}} \right) = {\left( {{\overset{\_}{T}}^{Indoor} - {\overset{\_}{T}}^{Outdoor}} \right)R^{Temp}}} & \; \\{\eta^{{HVAC}^{*}} = {\eta^{HVAC}R^{\eta}}} & \; \\{Q^{{Internal}^{*}} = {Q^{Internal}R^{Internal}}} & \;\end{matrix}$Divide Q^(Internal)* by η^(HVAC)* and multiply by the binary flagHeatOrCool to obtain Q^(Adj.Internal)*:

$\begin{matrix}\begin{matrix}{\frac{({HeatOrCool})\left( Q^{{Internal}^{*}} \right)}{\eta^{{HVAC}^{*}}} = \frac{({HeatOrCool})\left( Q^{Internal} \right)R^{Internal}}{\eta^{{HVAC}^{*}}}} \\{= Q^{{Adj}.{Internal}^{*}}}\end{matrix} & (19)\end{matrix}$Next, substitute in η^(HVAC)* from Equation (18):

$\begin{matrix}\begin{matrix}{Q^{{Adj}.{Internal}^{*}} = \frac{({HeatOrCool})\left( Q^{Internal} \right)R^{Internal}}{\eta^{HVAC}R^{\eta}}} \\{= \frac{Q^{{Adj}.{Internal}}R^{Internal}}{R^{\eta}}}\end{matrix} & (20)\end{matrix}$Substitute Equations (18) and (20) into Equation (16) and factor out

$\left( \frac{1}{R^{\eta}} \right)\text{:}$

$\begin{matrix}{Q^{{Fuel}^{*}} = {\quad\left\lbrack {\frac{({HeatOrCool})\left( {UA}^{Total} \right)\left( {{\overset{\_}{T}}^{Indoor} - {\overset{\_}{T}}^{Outdoor}} \right)(H)\left( {R^{UA}R^{{Temp})}} \right.}{\eta^{HVAC}} - {\left. \quad{Q^{{Adj}.{Internal}}R^{Internal}} \right\rbrack\left( \frac{1}{R^{\eta}} \right)}} \right.}} & (21)\end{matrix}$Substitute in Equation (15):

$\begin{matrix}\begin{matrix}{Q^{{Fuel}^{*}} = {\left\lbrack {{\left( {Q^{Fuel} + Q^{{Adj}.{Internal}}} \right)R^{UA}R^{Temp}} - {Q^{{Adj}.{Internal}}R^{Internal}}} \right\rbrack\left( \frac{1}{R^{\eta}} \right)}}\end{matrix} & (22)\end{matrix}$

Equation (22) can be used for evaluating investments that affect heating(or cooling) fuel consumption. This equation predicts future heating (orcooling) fuel consumption based on existing heating (or cooling) fuelconsumption, existing adjusted internal gains, as specified in Equation(7), and four ratios that express the relationship between the existingand post-change variables, as specified in Equation (17), can be set to1 if no changes. FIG. 12 is a flow diagram showing a method 130 forforecasting seasonal fuel consumption for indoor thermal conditioningusing the Approximated Thermal Performance Forecast approach with theaid of a digital computer in accordance with a further embodiment.Execution of the software can be performed with the assistance of acomputer system, such as further described infra with reference to FIG.23, as a series of process or method modules or steps.

Equation (22) has input six parameters. The amount of fuel consumed forthe heating (or cooling) season and the adjusted internal gains for theseason are required parameters; the four ratio terms that express therelationships between the existing and post-change variables for thebuilding properties can be set to equal 1 if there are no changes to bemade or evaluated. Setting the four ratio terms to equal 1 creates aparameterized form of Equation (22) into which changes to thermalconductivity, desired indoor temperature, internal heating gains, andthe HVAC system efficiency can later be input to model their effects onseasonal fuel consumption. In addition, solving the parameterized formof Equation (22) with the four ratio terms equal to 1 allows a baseseasonal fuel consumption value to be established, which is useful forcomparisons during subsequent analysis of proposed changes.

Historical seasonal fuel consumption is first obtained (step 131) andcan be measured, for example, directly from a customer's utility bills.Seasonal adjusted internal gains can be determined (step 132) usingdaily (or monthly) historical fuel consumption data combined withtemperature data, as further described infra with reference to FIG. 15.A parameterized form of the seasonal fuel consumption calculationexpression, Equation (22), is then created (step 133).

The effects on seasonal fuel consumption of proposed investments in thebuilding or thermal conditioning equipment can now be modeled. One ormore factors that represent a change in thermal conductivity, desiredindoor temperature, internal heating gains, or HVAC system efficiencyare accepted as input values (step 134). Each factor is expressed as aratio term with the changed value over the base value. The seasonalheating and cooling fuel consumption is then forecast as a function ofthe historical fuel consumption, the adjusted internal gains, and theinput ratio terms (step 135), as per Equation (22).

In a further embodiment, the creation of a parameterized form ofEquation (22) and calculation of a base seasonal fuel consumption valuecan be skipped. Instead, one or more of the four ratio terms arepopulated with actual values that reflect a change in their respectiveproperties, that is, those ratio terms do not equal 1, and are inputdirectly into Equation (22) to forecast seasonal fuel consumption basedon the one or more changes, albeit without the benefit of having a baseseasonal fuel consumption value to compare.

Example

As an example, consider an existing home that has a seasonal heatingfuel consumption Q^(Fuel) of 350 therms and existing adjusted internalgains Q^(Adj.Internal) of 200 therms. The homeowner is contemplating aset of investments with multiple interacting effects that include:

-   -   Increasing insulation and reducing infiltration losses that        results in a UA ratio R^(UA) of 50 percent.    -   Installing a smart thermostat that reduces average indoor        temperature from 68° F. to 66° F., so that the ratio of        temperature rise over the average outdoor temperature R^(Temp)        of 54° F. is 86 percent.    -   Making other electric efficiency investments that reduce the        internal gains 13, so that the internal gain ratio R^(Internal)        is 50 percent.    -   Installing a heat pump space heater that is four times as        efficient as the existing heater, so that the HVAC ratio R^(η)        is 400 percent.        Inputting these assumptions into Equation (22) reflects a        heating fuel consumption reduction from 350 therms to 34 therms:

$\begin{matrix}{Q^{{Fuel}^{*}} = {{\left\lbrack {{\left( {{350\mspace{14mu}{therms}} + {200\mspace{14mu}{therms}}} \right)(0.50)(0.86)} - {\left( {200\mspace{20mu}{therms}} \right)(0.50)}} \right\rbrack\left( \frac{1}{4} \right)} = {34\mspace{14mu}{therms}}}} & (23)\end{matrix}$This set of investments is also reflected in the graphs of thecumulative effect of five separate investments on a building discussedsupra with reference to FIG. 6 through FIG. 11.

Validation

Calculating the impact of a set of investments that have interrelatedeffects typically requires running a detailed model. From an investmentanalysis perspective, a simplified (but not simplistic) forecast couldbe beneficial. The simplifying assumption made in deriving Equation (22)was that the balance point temperature, and thus the length of theheating or cooling season, was not changed by the investments. Thissection assesses the effect of this simplifying assumption since certaintypes of investments will change the balance point temperature.

One way to make this assessment is to compare results from the DegreeDay approach with the Approximated Thermal Performance Forecast approachunder a range of scenarios for a sample house located in citiesthroughout the United States. The key assumptions for the scenarios arelisted in Table 1. The values in the Base Case column are estimates forthe sample house. The values in the Possible column correspond to whatthe values might be, given various investment alternatives and wereselected to represent extreme values to verify model robustness.

TABLE 1 Assumption Base Case Possible Winter Indoor 70° F. 66° F.Temperature Summer Indoor 70° F. 72° F. Temperature Heater 80% 320%Efficiency (or COP) Air Conditioning 12 24 SEER Building Thermal 800Btu/hr-° F. 400 Btu/hr-° F. Conductivity Internal Gains 3,912 Btu/hr1,956 Btu/hr

The Degree Day and Approximated Thermal Performance Forecasts approacheswere run independently and all combinations of Base Case and Possiblevalues were considered. For example, one scenario was to reduce thetemperature in the winter by 4° F. from 70° F. to 66° F. Anotherscenario was to combine two investments that increased heater efficiencyand reduced building thermal conductivity. In all, there were 64possible combinations with 128 values for each location since eachcombination was run using the two approaches. FIG. 13 is a set of graphsshowing, by way of examples, normalized results for seasonal fuelconsumption forecasts generated by the Approximated Thermal PerformanceForecast and Degree Day approaches for five different cities. Theresults are normalized to the base case Degree Day result. They-axiscorresponds to normalized results (as a percentile) for the ApproximatedThermal Performance Forecast and the x-axis corresponds to normalizedresults for the Degree Day approach (as a percentile). For example, thebase case Degree Day approach resulted in 78 MBtu being required for the2015 heating season in Washington, D.C. All heating season results forWashington, D.C. for both methods are normalized to the Base Case DegreeDay approach by dividing by 78 MBtu, which expresses the results inpercentage terms.

All of the scenario results would be along the dashed line if bothmethods produced identical results. As depicted in the graphs, there islittle difference between the Approximated Thermal Performance Forecastresults versus the corresponding Degree Day results, even with majorchanges to the building, except for the cooling season in Seattle, wherethere is more error because cooling needs in Seattle are minimal. Thisresults in magnification of percentage errors when expressed on arelative basis. Thus, the Approximated Thermal Performance Forecastapproach provides a good estimate of the effect of investment changesrelative to the Degree Day approach.

Observable Parameters

The Approximated Thermal Performance Forecast approach is based onobservable input data that includes heating (or cooling) fuelconsumption, and indoor and outdoor temperatures. In Equation (22), theamount of fuel consumed for heating (or cooling) Q^(Fuel) and adjustedinternal gains Q^(Adj.Internal) are required parameters; the fourremaining ratio parameters for change in thermal conductivity, change inindoor temperature, change in internal gains, and change in HVAC systemefficiency can be set to equal 1 if there are no changes to be made orevaluated.

TABLE 2 Basic All Solar Model Thermal Parameters Parameters GainsVerification Mass Parameters Q^(Fuel) ✓ ✓ ✓ ✓ ✓ Q^(Adj. Internal) ✓ ✓ ✓✓ ✓ Base value for R^(UA) ✓ ✓ ✓ ✓ Base value for R^(Temp) ✓ ✓ ✓ ✓ ✓ Basevalue for R^(Adj. Internal) ✓ ✓ ✓ ✓ Base value for R^(η) ✓ ✓ ✓ ✓ ThermalMass ✓ Input Data Est. or Meas. HVAC Eff. Yes Yes Yes Yes (%) FuelConsumption (kWh) Daily Daily Daily Daily Daily Avg. Outdoor Temp. (°F.) Daily Daily Daily Daily Daily Avg. Indoor Temp. (° F.) SeasonalSeasonal Seasonal Daily Daily Avg. Number of Occupants Seasonal SeasonalSeasonal Avg. Internal Electric (kW) Seasonal Daily Daily Avg.Irradiance (kW/m²) Seasonal Daily Daily Beginning Indoor Temp. Daily (°F.)

This section describes how to calculate the two required parametersbased on the available input data. Table 2 lists the parameters that canbe calculated based on the input data. Note that for the input data forfuel consumption, monthly fuel can be used in place of daily fuel ifdaily HVAC fuel consumption is not available. The calculations will beillustrated using data from the 2015-2016 heating season from Nov. 1,2015 to Mar. 31, 2016 for an efficient home located in Napa, Calif.

Basic Parameters

The amount of fuel consumed for the heating season (or cooling season)Q^(Fuel) and adjusted internal gains Q^(Adj.Internal) are requiredparameters in Equation (22). Adjusted internal gains Q^(Adj.Internal)can be calculated using daily (or monthly) historical fuel consumptiondata combined with average daily outdoor temperature. FIG. 14 is a flowdiagram showing a routine 140 for determining adjusted internal gainsfor use with the method 120 of FIG. 12. As with the Thermal PerformanceForecast approach, discussed supra, the average daily outdoortemperatures are obtained (step 141). The daily fuel consumption isplotted against the average daily outdoor temperature (step 142). Theslope of the plot is determined and divided by 24 hours to convert dailyfuel consumption to average daily fuel usage rate (step 143). Theconverted slope equates to the ratio of thermal conductivity over HVACsystem efficiency, that is,

$\frac{{UA}^{Total}}{\eta^{HCAC}}\mspace{14mu}{\left( {{step}\mspace{14mu} 144} \right).}$The x-intercept of the plot is also determined, which equates to thebalance point temperature (step 145), assuming that the internal gains13 are constant across the temperature range. Finally, the adjustedinternal gains Q^(Adj.Internal) are determined (step 146), per Equation(7), as a function of the applicable season (by setting the binary flagHeatOrCool to 1 for heating season and −1 for cooling season), the ratio

$\frac{{UA}^{Total}}{\eta^{HVAC}},$the average indoor temperature over the applicable season T ^(Indoor),the balance point temperature T^(Balance-Point) and the duration of theseason H (in hours).

An example can help illustrate the derivation of the adjusted internalgains. FIG. 15 is a graph 150 showing, by way of example, daily heatingfuel consumption versus average outdoor temperature for the heatingseason for the efficient house. The x-axis 151 represents the averagedaily outdoor temperature (in ° F.). The y-axis 152 represents dailyfuel consumption (in kWh per day). The slope of the plot 153, whenconverted to a fuel usage rate by dividing by 24 hours in a day, is0.115 kW per ° F. and the x-intercept is 60° F. Using Equation (7), theadjusted internal gains Q^(Adj.Internal) can be calculated as follows.Assume that the average indoor temperature was 68° F. The heatingseason, that is, HeatOrCool equals 1, had 3,648 hours with an averageoutdoor temperature of 51.1° F. Seasonal heating fuel consumption can becalculated by summing the daily values, which equaled 3,700 kWh for thesample home. Inputting these values into Equation (7) yields:

$\begin{matrix}{Q^{{Adj}.\;{Internal}} = {{(1)\left( {0.115\mspace{11mu}\frac{kW}{{^\circ}\mspace{11mu}{F.}}} \right)\left( {{68{^\circ}} - {60{^\circ}}} \right)\left( {3,648\mspace{14mu} h} \right)}\; = {3,350\mspace{14mu}{kWh}}}} & (24)\end{matrix}$

Thus, the adjusted internal gains Q^(Adj.Internal) is 3,350 kWh. Notethat HVAC system efficiency η^(HVAC) is not required for thiscalculation. Where there are large daily variations from the averageindoor temperature, such as occurs in an office building that isunoccupied and unheated during weekends and holidays, the season can bedefined to exclude weekend and holiday data.

With the two parameters, Q^(Fuel) and Q^(Adj.Internal), a parameterizedform of Equation (22) for determining predicted seasonal fuelconsumption Q^(Fuel)* for this particular house is:

$\begin{matrix}{Q^{{Fuel}^{*}} = {\quad{\left\lbrack {{\left( {{3,700\mspace{20mu}{kWh}} + {3,350\mspace{14mu}{kWh}}} \right)R^{UA}R^{Temp}} - {\left( {3,350\mspace{20mu}{kWh}} \right)R^{Intenal}}} \right\rbrack\left( \frac{1}{R^{\eta}} \right)}}} & (25)\end{matrix}$Now, future fuel consumption Q^(Fuel)* can now be predicted by inputtinginformation about the four ratios, the change in thermal conductivityratio R^(UA), the change in indoor temperature ratio R^(Temp), thechange in internal gains ratio R^(Internal) and the change in HVACsystem efficiency ratio R^(η). Suppose, for example, that a consumerwants to evaluate the effect of reducing the building's thermalconductivity by 50 percent, but everything else remains the same.Evaluating Equation (25) with a thermal conductivity ratio R^(UA) of 0.5yields:Q ^(Fuel)*=[(7,050 kWh)(0.5)(1)−(3,350 kWh)(1)](1/1)=175 kWh  (26)Thus, future fuel consumption Q^(Fuel)* would be 175 kWh, falling from3,700 kWh before the investment.

All Parameters

The previous section described how to calculate the two required inputparameters to Equation (22), seasonal fuel consumption Q^(Fuel) andadjusted internal gains Q^(Adj.Internal). The section also described thebase information needed to calculate the effect of a change in averageindoor temperature. The base value for the ratio term for the indoortemperature R^(Temp) is simply (T ^(Indoor)−T ^(Outdoor)).

The base values for the remaining three ratio terms, change in thethermal conductivity of the building R^(UA), change in the internalgains within the building R^(Internal), and change in the HVAC systemefficiency R^(η), can be calculated if the HVAC system efficiencyη^(HVAC) is specified. HVAC system efficiency η^(HVAC) can either beestimated or measured using an empirical test, such as described incommonly-assigned U.S. Pat. No. 10,339,232, cited supra. The base valuefor the ratio term for the change in thermal conductivity R^(UA) can becalculated by multiplying the ratio of thermal conductivity over HVACsystem efficiency

$\frac{{UA}^{Total}}{\eta^{HVAC}},$such as determined by plotting average daily fuel usage rate versus theaverage daily outdoor temperature, as described supra with reference toFIG. 14, by η^(HVAC). The base value for the ratio term for the changein internal gains R^(Internal) can be calculated by multiplying adjustedinternal gains Q^(Adj.Internal) by the HVAC system efficiency η^(HVAC)Finally, the base value for the ratio term for the change in HVAC systemefficiency R^(η) is simply the HVAC system efficiency η^(HVAC). For thesample home, the heating efficiency equals 100 percent since electricbaseboard heating is used. Thermal conductivity UA^(Total) equals 0.115kW/° F., average internal gains Q^(Internal) equals 0.918 kW, and HVACsystem efficiency η^(HVAC) equals 100 percent.

Solar Gains

Solar gains Q^(Solar) can be difficult to measure. Here, the sample homehad average internal gains from electricity Q^(Electric) of 0.302 kW andaverage solar radiation of 0.115 kW/m². The building averaged twooccupants that had heat gains of 0.147 kW. Inputting these values intoEquation (3) yields:

$\begin{matrix}{W = {\frac{{0.918\mspace{20mu}{kW}} - \left( {{0.302\mspace{25mu}{kW}} + {0.147\mspace{20mu}{kW}}} \right)}{0.115\;\frac{kW}{m^{2}}} = {4.1\mspace{11mu} m^{2}}}} & (27)\end{matrix}$Thus, the effective window area W is about 4.1 m².

Suppose that the consumer is considering whether to replace existingwindows with passive solar windows that will double the transmissivityto increase solar gains. The passive solar windows have the same R-valueas the existing windows. Current solar gains equal

${\left( {4.1\mspace{11mu} m^{2}} \right)\left( {0.115\;\frac{kWh}{m^{2}}} \right)} = {0.472\mspace{20mu}{{kW}.}}$Predicted solar gains would be

${\left( {8.2\mspace{14mu} m^{2}} \right)\left( {0.115\;\frac{kWh}{m^{2}}} \right)} = {0.944\mspace{14mu}{{kW}.}}$As a result, the internal gains ratio R^(Internal) will equal

$\frac{\left( {{0.302\mspace{14mu}{kW}} + {0.147\mspace{14mu}{kW}} + {0.472\mspace{14mu}{kW}}} \right) + {0.472\mspace{14mu}{kW}}}{\left( {{0.302\mspace{14mu}{kW}} + {0.147\mspace{14mu}{kW}} + {0.472\mspace{14mu}{kW}}} \right)} = {\frac{{0.921\mspace{14mu}{kW}} + {0.472\mspace{14mu}{kW}}}{0.921\mspace{14mu}{kW}} = {1.51.}}$

Set the internal gains ratio R^(Internal) in Equation (25) to 1.51 andset all other ratios equal to 1:Q ^(Fuel)*=7,050 kWh−(3,350 kWh)(1.51)=1,991 kWh  (28)Thus, the passive solar windows would reduce future fuel consumptionQ^(Fuel)* from 3,600 kWh to 1,991 kWh.

Model Verification

In the foregoing discussion, internal gains from electricityQ^(Electric) and internal gains from occupants Q^(Occupants) have beenassumed to be constant and internal solar gains Q^(Solar) have beenassumed to be proportional to irradiance.

These assumptions can be verified if daily internal electric andirradiance data are available. For the sample building, this data wasfed into an optimization program to solve for the thermal conductivityUA^(Total) and balance point temperature. Here, the thermal conductivitywas 0.109 kW/° F. and the balance point temperature was 60.3° F. FIG. 16and FIG. 17 are graphs 160, 170 showing, by way of example, predictedversus measured daily fuel consumption for the efficient house withthermal mass respectively excluded and included. In both graphs, thex-axis represents measured daily fuel consumption (in kWh). The y-axisrepresents predicted fuel consumption (in kWh). In the graph 160 of FIG.16, the daily predicted fuel consumption was determined using Equation(16). In the graph 170 of FIG. 17, the daily effect of thermal mass Mwas factored in using Equation (8) to add adjusted internal gainsQ^(Adj.Internal) (on a daily basis), after which the optimization wasrepeated. Here, the sample home had a thermal conductivity UA^(Total) of0.116 kW/° F., balance point temperature of 59.8° F., and thermal mass Mof 4.187 kWh/° F. FIG. 18 is a graph 180 showing, by way of example,predicted versus measured daily fuel consumption for the efficient houseover time. The x-axis represents each day over a five-month period.They-axis represents measured daily fuel consumption (in kWh per day).The measured and predicted fuel consumption values are fairly wellcorrelated throughout the time period.

Inclusion of thermal mass M is beneficial from several perspectives.First, in the situation of the sample home, including thermal mass Mreduces error by about one-third. Second, the inclusion of thermal massM is likely to increase accuracy of results for the input parameters.Finally, thermal mass is a key input parameter in optimizing HVAC systemefficiency, such as described in commonly-assigned U.S. Pat. No.10,203,674, issued Feb. 12, 2019, the disclosure of which isincorporated by reference. The foregoing approach presents a way tocalculate thermal mass M with only utility consumption, indoortemperature data, outdoor temperature data, and HVAC system efficiencyinputs are required parameters.

Example for Inefficient House

Consider another example using data from an inefficient house in Napa,Calif. over the same time period of the 2015-2016 heating season.Weekends were excluded because the house was used for business purposesonly. The average indoor temperature was 64.3° F. with 2,472 hours inthe heating season (with weekends excluded). Historical utility billsshow that fuel consumption was 13,100 kWh. HVAC heater efficiency wasassumed to be 80 percent.

TABLE 3 Basic Solar Thermal Parameters Gains Mass Balance Point 61° F.60.8° F. 60.4° F. Temp. Thermal 0.513 kW/° F. 0.518 kW/° F. 0.519 kW/°F. Conductivity Effective Window N/A 5.9 m² 7.5 m² Area Thermal Mass N/AN/A 10.486 kWh/° F. MAE Error N/A 24% 14%

Table 3 presents the results. In addition, FIG. 19 is a graph 190showing, by way of example, daily heating fuel consumption versusaverage outdoor temperature for the heating season for the inefficienthouse. The x-axis 131 represents the average daily outdoor temperature(in ° F.). The y-axis 132 represents daily fuel consumption (in kWh).Similarly, FIG. 20 and FIG. 21 are graphs 200, 210 showing, by way ofexample, predicted versus measured daily fuel consumption for theinefficient house with thermal mass respectively excluded and included.In both graphs, the x-axis represents measured daily fuel consumption(in kWh per day). The y-axis represents predicted fuel consumption (inkWh per day). Finally, FIG. 22, is a graph 220 showing, by way ofexample, predicted versus measured fuel consumption for the efficienthouse over time. The x-axis represents month. The y-axis representsdaily fuel consumption (in kWh). As with the efficient house, discussedsupra with reference to FIG. 15 through FIG. 18, the measured andpredicted fuel consumption values are fairly correlated throughout thetime period.

For the inefficient house, adjusted internal gains Q^(Adj.Internal)equal 6,250 kWh:

$\begin{matrix}{Q^{{Adj}.\;{Internal}} = {{\left( {0.649\;\frac{kW}{{^\circ}\mspace{14mu}{F.}}} \right)\left( {{64.3{^\circ}} - {60.4{^\circ}}} \right)\left( {2,472\mspace{20mu} h} \right)}\; = {6,250\mspace{14mu}{kWh}}}} & (29)\end{matrix}$Projected fuel consumption can be estimated to reflect the effect of newinvestments by inputting the adjusted internal gains Q^(Adj.Internal)(6,250 kWh) and heating fuel consumption (13,100 kWh) into Equation(22):

$\begin{matrix}{Q^{{Fuel}^{*}} = {\left\lbrack {{\left( {19{,350\mspace{20mu}{kWh}}} \right)R^{UA}R^{Temp}} - {\left( {6,250\mspace{20mu}{kWh}} \right)R^{Internal}}} \right\rbrack\left( \frac{1}{R^{\eta}} \right)}} & (30)\end{matrix}$Energy Consumption Modeling System

Forecasting seasonal fuel consumption for indoor thermal conditioning,as well as changes to the fuel consumption triggered by proposedinvestments in the building or thermal conditioning equipment with theThermal Performance Forecast and Approximated Thermal PerformanceForecast approaches can be performed with the assistance of a computer,or through the use of hardware tailored to the purpose. FIG. 23 is asystem 230 for forecasting seasonal fuel consumption for indoor thermalconditioning with the aid of a digital computer in accordance with oneembodiment. A computer system 231, such as a personal, notebook, ortablet computer, as well as a smartphone or programmable mobile device,can be programmed to execute software programs 232 that operateautonomously or under user control, as provided through user interfacingmeans, such as a monitor, keyboard, and mouse. The computer system 231includes hardware components conventionally found in a general purposeprogrammable computing device, such as a central processing unit,memory, input/output ports, network interface, and non-volatile storage,and execute the software programs 232, as structured into routines,functions, and modules. In addition, other configurations ofcomputational resources, whether provided as a dedicated system orarranged in client-server or peer-to-peer topologies, and includingunitary or distributed processing, communications, storage, and userinterfacing, are possible.

For the Thermal Performance Forecast approach, the computer system 231needs data on the average daily outdoor temperatures 233 and the balancepoint temperatures 234 for the heating 235 and cooling 236 seasons forthe building 237. The computer system 231 executes a software program232 to determine seasonal (annual) fuel consumption 238 using theThermal Performance Forecast approach, described supra with reference toFIG. 3 et seq.

For the Approximated Thermal Performance Forecast approach, the computersystem 231 needs the amount of fuel consumed for heating (or cooling)Q^(Fuel) 239 and adjusted internal gains Q^(Adj.Internal) 240 for theheating 235 and cooling 236 seasons for the building 237. The remainingbase values for thermal conductivity 241, indoor temperature 242,adjusted internal gains 243, and HVAC system efficiency 244 can then becalculated. The computer system 231 executes a software program 232 todetermine seasonal (annual) fuel consumption 238 using the ApproximatedThermal Performance Forecast approach described supra with reference toFIG. 12 et seq.

Applications

The two approaches, the Thermal Performance Forecast and theApproximated Thermal Performance Forecast, to estimating fuelconsumption for heating (or cooling) on an annual or seasonal basisprovide a powerful set of tools that can be used in variousapplications. A non-exhaustive list of potential applications will nowbe discussed. Still other potential applications are possible.

Application to Thermal Conditioning Analysis

The derivation of adjusted internal gains, effective window area, andfuel consumption can have applicability outside the immediate context ofseasonal fuel consumption forecasting. Fundamental building thermalproperty parameters, including thermal conductivity UA^(Total),effective window area W, and thermal mass M, that are key input valuesto various methodologies for evaluating thermal conditioning costs andinfluences can all be determined using at most utility consumption,outdoor temperature data, indoor temperature data, and HVAC systemefficiency as inputs. For instance, these parameters can be input intotime series modelling approaches to forecast hourly fuel consumption,such as described in commonly-assigned U.S. Pat. No. 10,339,232, citedsupra.

Quantifying a building's thermal conductivity remains a non-trivialtask. A building's thermal conductivity can be estimated through anenergy audit or empirically determined through a short-durationcontrolled test. Alternatively, the ratio of thermal conductivity overHVAC system efficiency

$\frac{{UA}^{Total}}{\eta^{HVAC}},$as reflected by the slope of a plot of average daily fuel usage rateversus average daily outdoor temperatures over a season, as discussedsupra with reference to FIG. 14, can be used to quantify thermalconductivity UA^(Total) without any audit or empirical testing required,provided that HVAC system efficiency is known.

Similarly, effective window area W is the dominant means of solar gainin a typical building during the winter and includes the effect ofphysical shading, window orientation, the window's solar heat gaincoefficient, as well as solar heat gain through opaque walls and roofs.Quantifying effective window area W typically requires physicallymeasuring vertical, south-facing window surfaces or can be empiricallydetermined through a series of sequentially-performed short durationtests. Alternatively, per Equation (3), the effective window area W canbe calculated based on overall internal gains Q^(Internal), internalgains from electricity Q^(Electric), internal gains from occupantsQ^(Occupants), and the available solar resource Solar, again without anyaudit or empirical testing required.

Thermal mass can be estimated by selecting the thermal mass that reducesthe error between predicted and measured fuel consumption, asillustrated in FIG. 16 and FIG. 17, and in FIG. 20 and FIG. 21. Thisderivation of thermal mass avoids an on-site visit or special control ofthe HVAC system.

Application to Homeowners

Both of the approaches are especially useful to homeowners and theaverage consumer due to their intuitive appeal. By keeping weather dataseparate from user preferences and building-specific parameters, theThermal Performance Forecast approach permits the effects of proposedinvestments in the building or thermal conditioning equipment to bevisualized with the impact of those investments on fuel consumptionreadily apparent. The Approximated Thermal Performance approach allowschanges to thermal conductivity, indoor temperature, internal gains, andHVAC system efficiency to be modeled with only two input parameters, theamount of fuel consumed for the heating season (or cooling season)Q^(Fuel) and the adjusted internal gains Q^(Adj.Internal). As discussedsupra with reference to Table 1, these four changes respectivelycorrelate, for instance, to popular energy-saving investments thatinclude:

-   -   Smart thermostat (245): reduce indoor temperature in the winter;        increase indoor temperature in the summer.    -   Electric heat pump (246): convert from a natural gas heater to        an electric heat pump to increase heater efficiency.    -   Increased insulation and improved building sealing (247): reduce        building thermal conductivity.    -   Improved appliances (248): reduce internal gains by making        energy efficiency investments in improved appliances.        The first three investments reduce fuel consumption. The energy        efficiency investments increase heating fuel consumption and        reduce air conditioning fuel consumption by reducing internal        gains.

Application to Building Shell Investment Valuation

The economic value of heating (and cooling) energy savings associatedwith any building shell improvement in any building has been shown to beindependent of building type, age, occupancy, efficiency level, usagetype, amount of internal electric gains, or amount solar gains, providedthat fuel has been consumed at some point for auxiliary heating.

While the invention has been particularly shown and described asreferenced to the embodiments thereof, those skilled in the art willunderstand that the foregoing and other changes in form and detail maybe made therein without departing from the spirit and scope.

The invention claimed is:
 1. A system for forecasting fuel consumptionfor indoor thermal conditioning using thermal performance forecastapproach with the aid of a digital computer, comprising: a computercomprising a processor and a memory coupled to the processor and storingcomputer-executable code, the computer configured to: obtain averagedaily outdoor temperatures for a time period; obtain historical dailyfuel consumption for the time period; convert the historical daily fuelconsumption into an average daily fuel usage rates for the time period;generate a continuous frequency distribution of occurrences of theaverage daily outdoor temperatures; create a plot of the daily fuelusage rates versus the average daily outdoor temperatures; identify oneor more balance point temperatures for the building for the time period;and calculate fuel consumption for at least a portion of the time periodbased on sampling the daily fuel usage rate along a range of averagedaily outdoor temperatures times the temperatures' respectivefrequencies of occurrence and further based on one or more of thebalance point temperatures.
 2. A system according to claim 1, whereinthe fuel consumption for the time period is determined in accordancewith:$Q^{Fuel} = {\int_{0{^\circ}\mspace{14mu} R}^{T^{\text{Balance}\text{-}\text{Point}}}\frac{{{UA}^{Total}\left( {T^{\text{Balance}\text{-}\text{Point}} - T^{Outdoor}} \right)}{f(T)}(8760){dT}}{\eta^{\text{HVAC}\text{-}\text{Heating}}}}$where η^(HVAC-Heating) is the efficiency of the HVAC system for heating,T^(Balance-Point) is one of the balance point temperatures, UA^(Total)is the building's thermal conductivity, 0° R is zero degrees Rankine,and f(T) is the continuous frequency distribution.
 3. A system accordingto claim 1, wherein the time period comprises a heating season and acooling season and the one or more balance point temperatures comprisethe balance point temperature for the heating season and the balancepoint temperature for the cooling season within the year.
 4. A systemaccording to claim 3, the computer further configured to: display thebalance point temperatures for the heating season and the cooling seasonon the plot; and display frequencies of the average daily outdoortemperatures as an axis of the plot.
 5. A system according to claim 4,the computer further configured to: model a change to a thermalconditioning of the building; and change the plot based on the modeling.6. A system according to claim 4, wherein the change comprises one ormore of an installation of a smart thermostat within the building,changing a fuel-based heater within the building to a heat-pump basedheater, an installation of an air conditioning system with a heat pumpinto the building, changing R-values of walls of the building, andchanging operation of electrical devices within the building.
 7. Asystem according to claim 1, the computer further configured to: obtainoutside temperature data in an hourly format for the time period; andconvert the outside temperature data into the average daily outdoortemperatures.
 8. A method for forecasting fuel consumption for indoorthermal conditioning using thermal performance forecast approach withthe aid of a digital computer, comprising the steps of: obtainingaverage daily outdoor temperatures for a time period; obtaininghistorical daily fuel consumption for the time period; converting thehistorical daily fuel consumption into an average daily fuel usage ratesfor the time period; generating a continuous frequency distribution ofoccurrences of the average daily outdoor temperatures; creating a plotof the daily fuel usage rates versus the average daily outdoortemperatures; identifying one or more balance point temperatures for thebuilding for the time period; and calculating fuel consumption for atleast a portion of the time period based on sampling the daily fuelusage rate along a range of average daily outdoor temperatures times thetemperatures' respective frequencies of occurrence and further based onone or more of the balance point temperatures, wherein the steps areperformed by a suitably-programmed computer.
 9. A method according toclaim 8, wherein the fuel consumption for the time period is determinedin accordance with:$Q^{Fuel} = {\int_{0{^\circ}\mspace{14mu} R}^{T^{\text{Balance}\text{-}\text{Point}}}\frac{{{UA}^{Total}\left( {T^{\text{Balance}\text{-}\text{Point}} - T^{Outdoor}} \right)}{f(T)}(8760){dT}}{\eta^{\text{HVAC}\text{-}\text{Heating}}}}$where η^(HVAC-Heating) is the efficiency of the HVAC system for heating,T^(Balance-Point) is one of the balance point temperatures, UA^(Total)is the building's thermal conductivity, 0° R is zero degrees Rankine,and f(T) is the continuous frequency distribution.
 10. A methodaccording to claim 8, wherein the time period comprises a heating seasonand a cooling season and the one or more balance point temperaturescomprise the balance point temperature for the heating season and thebalance point temperature for the cooling season within the year.
 11. Amethod according to claim 10, further comprising: displaying the balancepoint temperatures for the heating season and the cooling season on theplot; and displaying frequencies of the average daily outdoortemperatures as an axis of the plot.
 12. A method according to claim 11,further comprising: modeling a change to a thermal conditioning of thebuilding; and changing the plot based on the modeling.
 13. A methodaccording to claim 11, wherein the change comprises one or more of aninstallation of a smart thermostat within the building, changing afuel-based heater within the building to a heat-pump based heater, aninstallation of an air conditioning system with a heat pump into thebuilding, changing R-values of walls of the building, and changingoperation of electrical devices within the building.
 14. Anon-transitory computer readable storage medium storing code forexecuting on a computer system to perform the method according to claim8.